Answer:
( , 0) and (8,
)
Step-by-step explanation:
Curve is concave downward when the second derivative is negative.
y' = , by the Fundamental Theorem of Calculus
y'' = , which has a denominator that is always positive. The numerator
is negative when x > 0 and when x < 8. So that is when y'' is negative, and consequently when the curve y is concave down.
The y-intercept of the function is $50 and it represents the fixed amount for the labor charges.
<h3>How to find the y-intercept of a graph?</h3>
From the attached graph, we see that the x-axis is represented by time in hours while the y-axis is represented by labor charges in dollars.
Now, from the graph we see that the coordinates are;
(0, 50), (1, 125), (2, 200), (3, 275), (4, 350)
Now, the y-intercept of a linear graph is simply the point at which the graph crosses the y-axis.
In this graph attached, we see that the y-intercept is at the coordinate (0, (0, 50).
Thus, we conclude that the y-intercept of the function is $50 and it represents the fixed amount for the labour charges.
Read more about y-intercept at; brainly.com/question/26509774
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Note: The image of G after the dilation must be G'(5,-5) instead of G'(5,5).
Given:
The vertices of a rectangle are E(4,8), F(2,8), G(2,-2) and H(-4,-2).
The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,-5).
To find:
The algebraic representation that represents this dilation.
Solution:
If a figure is dilated by factor k with origin as the center of dilation, then the dilation is defined as:
...(i)
Let the given rectangle is dilated by factor k with origin as the center of dilation. Then,
The image of G after dilation is G'(5,-5). So,
On comparing both sides, we get
So, the scale factor is .
Substituting in (i), we get
Therefore, the required algebraic representation to represents this dilation is .